His agreement leaves 18 players still headed to arbitration hearings, which run from Tuesday through Feb. 21.
Story, 27, remains eligible to become a free agent following the 2021 World Series. He hit 35 homers and swiped 23 bases last season. He also set career highs in runs (111), batting average (.294) and on-base percentage (.363).
His goals for 2020 include stealing more bases and being more of a vocal leader.
"Leading by example is more natural for me," Story said last weekend during the fan fest at Coors Field. "But I think it's a total evolution of me trying to be the player I want to be."
Story is a career .276 hitter since making his debut in April 2016. He was a first-round draft pick in 2011.
The Rockies are trying to rebound from a 71-91 campaign after making the playoffs two years in a row. They've been quiet on the free-agent front all winter.
But they have made quite a bit of noise over the constant speculation that standout third baseman Nolan Arenado could be traded. Story doesn't think the Arenado situation will be a distraction heading into spring training.
"Whatever happens, we'll do a good job of handling it," Story said last weekend. "We're all pros here and we'll continue that way."